Hamilton `-cycles in Uniform Hypergraphs

We say that a k-uniform hypergraph C is an `-cycle if there exists a cyclic ordering of the vertices of C such that every edge of C consists of k consecutive vertices and such that every pair of consecutive edges (in the natural ordering of the edges) intersects in precisely ` vertices. We prove that if 1 ≤ ` < k and k − ` does not divide k then any k… CONTINUE READING